Composing and Decomposing Numbers: practice solutions, Kindergarten – download the PDF

1 Counting two colors ★★★

There are 6 orange counters and 3 blue counters. We put them together: \(6 + 3 = 9\).

There are 9 counters in all.

2 Ways to break apart 4 ★★★

We look for two numbers that make 4: \(4 = 1 + 3\), \(4 = 2 + 2\) and \(4 = 3 + 1\).

There are 3 ways if we do not use zero.

3 Fingers on two hands ★★★

The whole is 5. One part is 3. We need the other part: \(3 + 2 = 5\).

Ana has 2 fingers on her right hand.

4 How many empty spaces? ★★★

We count the empty squares: there are 2. So \(8 + 2 = 10\).

2 more counters fill the frame.

5 Ten and some ones ★★★

A full frame is 10. Add the 3 extra counters: \(10 + 3 = 13\).

Mia shows the number 13.

6 True or false? ★★★

1. 4 and 3 make 7, so it is true.
2. 5 and 5 make 10, not 9, so it is false.
3. 2 and 4 make 6, so it is true.

7 Missing part in a bond ★★★

The whole is 8 and one part is 5. We need \(5 + \square = 8\). Count up from 5: 6, 7, 8. That is 3 steps.

The missing part is 3, and \(8 = 5 + 3\).

8 Pairs that make 10 ★★★

1. \(3 + 7 = 10\), so the missing number is 7.
2. \(6 + 4 = 10\), so the missing number is 4.
3. \(9 + 1 = 10\), so the missing number is 1.
4. \(5 + 5 = 10\), so the missing number is 5.

9 Seeds in a garden ★★★

The whole is 10 seeds. One part is 6. We need \(6 + \square = 10\).

Since \(6 + 4 = 10\), Maya plants 4 seeds in the second row.

10 Another way to make 5 ★★★

1. There are 2 orange counters and 3 blue counters: \(5 = 2 + 3\).
2. Many answers are possible. For example, \(5 = 1 + 4\) or \(5 = 4 + 1\).

11 Which teen number? ★★★

1. The full frame is 10 and the second frame has 6 counters: \(10 + 6 = 16\).
2. The teen number is 16.

12 Muffins in a box ★★★

We compose a teen number: a full ten and 8 extra ones.

\(10 + 8 = 18\). There are 18 muffins in all.

13 Break apart 15 ★★★

15 is a full ten and some extra ones. If we take away the ten, 5 ones are left.

\(15 = 10 + 5\). The missing number is 5.

14 Which one does not belong? ★★★

\(3 + 4 = 7\), \(5 + 2 = 7\) and \(1 + 6 = 7\). But \(6 + 2 = 8\).

The pair that does not belong is \(6 + 2\).

15 Counting up to 14 ★★★

1. \(7 + 3 = 10\), so he adds 3 counters to fill the frame.
2. \(10 + 4 = 14\), so he adds 4 more counters.

In all he adds \(3 + 4 = 7\) counters, and \(7 + 7 = 14\).

16 Mystery teen numbers ★★★

1. A ten and 7 ones is \(10 + 7 = 17\). I am 17.
2. First put the extra counters together: \(2 + 6 = 8\). Then \(10 + 8 = 18\). I am 18.

17 Find the mistake ★★★

\(9 + 1 = 10\) is correct. But \(10 + 2 = 12\), not 13.

The first sentence is wrong. The right equation is \(13 = 10 + 3\).

18 All the ways to make 6 ★★★

We go up from 1: \(6 = 1 + 5\), \(6 = 2 + 4\), \(6 = 3 + 3\), \(6 = 4 + 2\), \(6 = 5 + 1\).

There are 5 ways.

19 Checking decompositions of 12 ★★★

1. A ten and 2 ones make 12, so it is true.
2. \(7 + 5 = 12\), so it is true.
3. \(6 + 5 = 11\), not 12, so it is false.

20 Toy cars ★★★

The whole is 16 and one part is 10. We need \(10 + \square = 16\).

A ten and 6 ones make 16, so \(16 = 10 + 6\). Sam has 6 blue cars.

21 Stickers in two pockets ★★★

We try pairs that make 9: \(8 + 1\), \(7 + 2\), \(6 + 3\), \(5 + 4\).

Only \(5 + 4\) has a difference of 1. The left pocket has 5 stickers and the right pocket has 4 stickers. Check: \(5 + 4 = 9\).

22 Fill the frame, then keep going ★★★

1. \(4 + 6 = 10\), so he adds 6 counters.
2. To reach 13 he needs 3 more beyond the ten: 3 counters.
3. \(13 = 10 + 3\).